CS100J / Fall 2002

Programming Assignment 1

Due: Tuesday, September 10

Goals

This assignment has two parts that will help you become familiar with Java, Matlab, and the CodeWarrior (CW) programming environment. You do not need to know how to program to do the assignment. You must complete both parts to receive full credit.  

Resources

The following resources contain answers to questions you may have in doing this assignment:

Course Materials:

http://www.cs.cornell.edu/Courses/cs100j/2002fa/material.htm          

Facilities:

http://www.cs.cornell.edu/Courses/cs100j/2002fa/facilities.htm          

Projects:

 http://www.cs.cornell.edu/Courses/cs100j/2002fa/projects.htm 

Guide to CodeWarrior Java for CS100:

http://www.cs.cornell.edu/Courses/cs100/2001su/guide/guide.html           

Online Help from inside CodeWarrior (if Help is  installed):

Help | CodeWarrior

Help | IDE | Create new projects | stationery

Motivation

Take any positive integer and do the following: if the integer is even, divide it by 2; otherwise multiply it by 3 and add 1. Repeat the process as long as the value remains greater than 1. For example, suppose you start with 11. Then the sequence you get is: 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.

It has long been conjectured that regardless of the starting point, you will always reach 1, but so far, no one has ever been able to prove this. Like Fermat's Last Theorem, which stumped researchers for many years, this deceptively simple statement is hard to prove or disprove.

In this assignment, you are given a Java program to enter and run that computes such sequences.  The program can be used to experiment with these mysterious sequences. We also show you how to plot the sequences using Matlab.

If you find an integer for which the attached program runs forever (and you haven't made a typo in entering the program), you have found a counter-example to the conjecture and will become famous. Call the New York Times.

Part 1: Java

Do the following tasks for this part: 

  1. Familiarize yourself with the pages and guides listed above under Resources. Refer to them, as necessary, in doing the assignment.

  2. Start CodeWarrior and create a new project for this assignment as follows:
    • Select File | New.
    • Select Java Stationery (or Java J2SE Stationery), enter the project name CS100P1, and click OK.
    • Click "+" to open the tab for the most recent version of the JDK, select Java Application, and click OK.

    (If you don't know how to do this, or don't understand what you are being asked to do, repeat step 1.)

  3. Obtain a copy of file TokenReader.java from the web and save it on your personal floppy disk, or if you are using your own computer, save it on your hard disk.

  4. Add TokenReader.java to your project using command Project|Add Files. If offered a dialog box with several checked target options, just click OK.

  5. Open the project source file TrivialApplication.java, as follows:
    • Click "+" next to Sources.
    • Double click TrivialApplication.java to open it.

  6. Edit the contents of the file TrivialApplication.java so that it exactly matches the program on the attached sheet. One way you can do this is to erase the unnecessary text from the stationery, and type the additional text given on the attached sheet. Another way you can do it is to erase the entire text of the stationery, and type the entire text given on the attached sheet. A third way is to is to erase the entire text of the stationery, and then cut and paste the program text out of the web page.

    Reminder: Carefully maintain the EXACT punctuation and capitalization -- Java is case-sensitive! However, the spacing and indentation matter only for style and do not need to perfectly match. Enter you name, ID, and section. If you have a partner, do the same for your partner. While entering program text, it is a good idea to save your work on disk frequently (using File|Save) in case you inadvertently erase everything.

  7. Select Project|Compile. Does a window pop-up warning you of compiler errors, also known as syntax errors? If so, carefully review the statements inside your code since, most likely, you typed something wrong. Repeatedly correct errors and reinvoke Project|Compile until you finally get no error messages. If by some miracle you have not made any typing errors, intentionally make one and invoke Project|Compile to see what happens.

  8. When finished correcting your typing-errors, select Project|Run. When prompted, enter the integer 10 and confirm that your program generates the output:

    5 after dividing by 2

    8 after dividing by 2

    4 after dividing by 2

    2 after dividing by 2

    1 after dividing by 2

    Done!

  9. Modify the program so that it produces output for the odd cases as well as the even cases. For instance, for the input 10, the modified program should produce the output:

    5 after dividing by 2

    16 after multiplying by 3 and adding 1

    8 after dividing by 2

    4 after dividing by 2

    2 after dividing by 2

    1 after dividing by 2

    Done!

    Hint: Refer to the code that generates output for the even case. In Java, the next one statement following the else keyword is executed when the if-condition is false. If you wish to execute several statements when the if-condition is false, you must enclose the list of statements in curly braces {}, just as in the even case.

  10. Test your code again by compiling and running it. Be sure to fix any bugs you may have introduced.

  11. Run the program with each of the following inputs.  For each input, try to understand what happens and why:

    0

    i.e., the number zero

    -19

    i.e., a negative number

    four

    i.e., text

    10,11,12

    i.e., a list of integers

    4/2

    i.e., an arithmetic expression

    12345678900

    i.e., an integer too big to store in an int variable

    1234567890

    i.e., a large integer that is not too big to store in an int variable

    123456789

    i.e., a large integer

     

    "Large" integers might run a "really long time." To stop your program on a PC, click on the close-box (the icon with the letter X inside) and select End Task in the dialog box that pops up. To stop the program on a Mac, press Option-Command-Escape, as explained in the CW guide.

  12. Run your modified code for integer input of 11. Print the modified program. Print the output for running your program with the input of 11.

  13. Remember to save your program to your own floppy disk if you are using a public machine.

Part 2: Matlab

This part will very briefly introduce some aspects of Matlab by plotting data you computed in Part 1 of this assignment. Matlab provides a very convenient and powerful software tool for data analysis, which typically involves plots of data. Plotting your data from Part 1 will demonstrate how the algorithm you programmed converges upon the integer 1. Note: Pressing Enter means pressing either the Enter or Return key.

1.       Consult your tip sheets and run Matlab.

2.       You should see a command window pop-up. This is where you will enter commands. Note: Do NOT type the prompt >>. Enter commands after the >>.

3.       Enter the following command statements to generate a plot of your test case from Part 1, Problem 9.

>> plot([11 34 17 52 26 13 40 20 10 5 16 8 4 2 1])

 This command creates the initial plot of your data. The data is plotted on the vertical (Y) axis. Press the Enter key after typing the input. A graphics window containing your plot should pop-up.

>> xlabel('count')

This command labels the horizontal (X) axis with text. Press Enter after typing.

>> ylabel('k')

This command labels the Y-axis. Press Enter after typing.

>> title('HW1: <type your name(s) here>')

This command titles your plot with text. You should enter something like title(`HW1: Pat Smith'). Press Enter after typing.

Matlab will automatically "update" (modify) your plot each time you press Enter.

4.       Print out your plot.

What to Hand In

Staple the following sheets together:

·         P1 Grading Guide (print out from http://www.cs.cornell.edu/Courses/cs100j/2002fa/projects.htm)

·         Printout of the final Java program, signed by you (and your partner).

·         Printout of the output from running the Java program with input of 11.

·         Printout of the Matlab plot.

Grading

See http://www.cs.cornell.edu/Courses/cs100j/2002fa/projects.htm for explanations of due-date and grading policies.

// Name:                        Partner's Name:

// ID:                          Partner's ID:

// Section:                   Partner's Section:

// Date:

// Project: CS100J/Fall 2002 P1

 

/* Input any integer and repeatedly divide it by 2 if even and

 * multiply it by 3 and add 1 if odd. Stop on reaching 1 or less.

 */

import java.io.*;

 

public class TrivialApplication {

    public static void main(String args[])

    {

      int k;

      String temp;

 

      // initialize Text object in to read from standard input.

         TokenReader in = new TokenReader(System.in);

   

      // Read and write some numbers and strings

         System.out.println("Please enter an integer: ");

   

      // Read integer

         k = in.readInt();

               

      // Perform algorithm

        while ( k > 1 )

            if ( (k % 2 ) == 0) {  // test if k is even

                 k = k / 2;

                 System.out.println(k + " after dividing by 2");

            }

            else

                 k = 3 * k + 1;

    System.out.println("Done!");

    }

}